Medical Sciences: cram pack

Formula sheets, the key method steps for every topic and 14 practice problems, with full solutions at the back.

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1Formulas and methods

Arterial blood gas interpretation

Normal ranges
pH 7.35–7.45, PaCO₂ 35–45 mmHg (4.7–6.0 kPa), HCO₃⁻ 22–26 mmol/L
ROME
Respiratory: PaCO₂ opposite to pH; Metabolic: HCO₃⁻ equal to pH
Winter’s formula
PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2
Metabolic alkalosis
PaCO₂ ≈ 0.7·HCO₃⁻ + 21
Anion gap
AG = Na⁺ − (Cl⁻ + HCO₃⁻) ≈ 8–12
Albumin-corrected gap
AG + 2.5·(4.0 − alb g/dL) = AG + 0.25·(40 − alb g/L)
Delta ratio
(AG − 12)/(24 − HCO₃⁻)
P/F ratio
PaO₂/FiO₂
Alveolar gas equation
PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8
Serum osmolality
2·Na⁺ + glucose + urea (2·Na⁺ + glucose/18 + BUN/2.8)

Method

  1. Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
  2. Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
  3. Look at the other value: normal means uncompensated, abnormal in the compensating direction means partial compensation, and a normal pH with both abnormal means full compensation.
  4. In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
  5. Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.

ECG rhythm strip interpretation

Paper (25 mm/s, 10 mm/mV)
1 small box = 0.04 s, 1 large box = 0.20 s, 10 mm = 1 mV
Heart rate, regular rhythm
300 ÷ large boxes = 1500 ÷ small boxes = 60 ÷ RR (s)
Heart rate, irregular rhythm
QRS complexes in 6 s × 10
Normal PR interval
0.12–0.20 s
Normal QRS duration
< 0.12 s
QTc (Bazett)
QT/√RR
QTc (Fridericia)
QT/∛RR
QTc (Framingham)
QT + 154·(1 − RR)
Sinus rates
bradycardia < 60, normal 60–100, tachycardia > 100 /min
Escape rates
junctional 40–60, ventricular 20–40 /min
Fast rhythms
SVT 150–250 /min (narrow), VT > 100 /min (wide)

Method

  1. Rate: for a regular rhythm divide 300 by the large boxes or 1500 by the small boxes between two R waves; for an irregular rhythm count the QRS complexes in 6 seconds and multiply by 10.
  2. Rhythm: compare the R–R intervals. Equal is regular; a repeating pattern is regularly irregular; no pattern at all is irregularly irregular.
  3. P waves: is there an upright P wave in lead II before every QRS, all alike? Look for fibrillatory or sawtooth waves, inverted P waves and P waves without a QRS.
  4. PR interval: from the start of P to the start of the QRS, normally 0.12–0.20 s and constant. Watch whether it lengthens, stays fixed before a dropped beat, or varies at random.
  5. QRS duration: below 0.12 s is narrow; 0.12 s or more is wide. Then name the rhythm, and for the QT use QTc = QT/√RR (Bazett) with times in seconds.

Evidence-based practice statistics

Sensitivity and specificity
Se = a/(a + c), Sp = d/(b + d)
Predictive values
PPV = a/(a + b), NPV = d/(c + d)
Accuracy
(a + d)/n
Likelihood ratios
LR+ = Se/(1 − Sp), LR− = (1 − Se)/Sp
PPV at prevalence p
Se·p / (Se·p + (1 − Sp)(1 − p))
Odds
odds = p/(1 − p); p = odds/(1 + odds); post-test odds = pre-test odds × LR
Risk measures
RR = EER/CER, ARR = CER − EER, RRR = ARR/CER
Number needed to treat
NNT = 1/ARR, rounded up; NNH = 1/(EER − CER)
Odds ratio
OR = ad/(bc)
Incidence rate
new cases / person-time

Method

  1. Draw the 2 × 2 table and label a, b, c and d before you calculate.
  2. Read sensitivity and specificity down the columns, predictive values along the rows.
  3. For another prevalence, imagine 10 000 people and fill the table with Se, Sp and the prevalence.
  4. For a likelihood ratio, convert the probability to odds, multiply, and convert back.
  5. For a trial, find EER and CER first; then RR = EER/CER, ARR = CER − EER and NNT = 1/ARR rounded up.

2Practice problems

1.Human anatomyMedium

The sympathetic nervous system leaves the central nervous system from which spinal segments?

  1. ACervical only
  2. BThoracic and upper lumbar (T1–L2)
  3. CSacral only (S2–S4)
  4. DCranial and sacral
2.Human anatomyHard

A large central disc prolapse at L4–L5 causes saddle anaesthesia, urinary retention and bilateral leg weakness. Which structure is compressed?

  1. AFemoral nerve
  2. BThoracic spinal cord
  3. CSciatic nerve in the buttock
  4. DCauda equina
3.Human physiologyMedium

How is the ejection fraction calculated?

  1. AStroke volume ÷ end-diastolic volume
  2. BEnd-systolic volume ÷ stroke volume
  3. CCardiac output ÷ heart rate
  4. DEnd-diastolic volume ÷ end-systolic volume
4.Human physiologyHard

After several days of persistent vomiting of stomach contents, which acid–base disturbance is most likely?

  1. AMetabolic acidosis
  2. BRespiratory acidosis
  3. CMetabolic alkalosis
  4. DRespiratory alkalosis
5.MicrobiologyMedium

Transfer of bacterial genes from one bacterium to another by a virus is called:

  1. ATranscription
  2. BConjugation
  3. CTransformation
  4. DTransduction
6.MicrobiologyHard

A child develops bloody diarrhoea after eating an undercooked burger, then a week later has kidney failure, anaemia and a low platelet count. Which organism is most likely?

  1. AClostridium perfringens
  2. BShiga toxin-producing E. coli such as O157:H7
  3. CStaphylococcus aureus
  4. DRotavirus
7.PharmacologyMedium

How should a hyoscine (scopolamine) patch for motion sickness be used?

  1. AApply it behind the ear several hours before travel
  2. BSwallow it if no water is available
  3. CApply it to the chest only after the vomiting has started
  4. DCut it in half for children without advice
8.PharmacologyHard

A breastfeeding mother needs a mild analgesic. Which drug is generally considered compatible with breastfeeding?

  1. AAspirin
  2. BParacetamol (acetaminophen)
  3. CCodeine (as co-codamol)
  4. DPethidine (meperidine)
9.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 73 mmHg (9.7 kPa). Use the rule that in acute respiratory acidosis HCO₃⁻ rises by 1 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 73 mmHg (9.7 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
10.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 34 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 34 mmol/L
PaCO₂ = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval and the R–R interval on this regular lead II strip, then calculate the rate-corrected QTc with Fridericia’s formula QTc = QT/∛RR (both in seconds). Give the answer in seconds to three decimals.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QTc = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVasystoleventricular fibrillationsinus bradycardiapulseless electrical activity (PEA)

A monitored patient is found unresponsive and not breathing normally, and no carotid pulse can be felt. The monitor shows this organised rhythm. What is this situation called? Click your answer.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1asystole
  2. 2ventricular fibrillation
  3. 3sinus bradycardia
  4. 4pulseless electrical activity (PEA)
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment1958051000abcontrol156244400cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 1000 patients received a new treatment and 400 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the absolute risk reduction ARR as a percentage. Round to one decimal place.

treatment: 195/1000control: 156/400
ARR = %
14.Evidence-based practice statisticsHard
pre-test20%post-test?p′LR+

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 20% for a disease. A test with sensitivity 82% and specificity 86% comes back positive. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 20%Se = 82%Sp = 86%positive
p′ = %

3Solutions

1.Human anatomy

Answer: B · Thoracic and upper lumbar (T1–L2)

Why this is the answer

Sympathetic preganglionic neurons lie in the lateral horn from T1 to L2. The parasympathetic system has a craniosacral outflow.

Answer

B · Thoracic and upper lumbar (T1–L2)
2.Human anatomy

Answer: D · Cauda equina

Why this is the answer

Below L1–L2 the canal holds the cauda equina. Central compression of these lumbar and sacral roots causes cauda equina syndrome, a surgical emergency.

Answer

D · Cauda equina
3.Human physiology

Answer: A · Stroke volume ÷ end-diastolic volume

Why this is the answer

Ejection fraction is the proportion of blood in the full ventricle that is ejected per beat. A normal value is about 55–70%.

Answer

A · Stroke volume ÷ end-diastolic volume
4.Human physiology

Answer: C · Metabolic alkalosis

Why this is the answer

Vomiting removes HCl, and the stomach's acid secretion leaves bicarbonate in the blood. Volume loss and low potassium help keep the alkalosis going.

Answer

C · Metabolic alkalosis
5.Microbiology

Answer: D · Transduction

Why this is the answer

In transduction a bacteriophage accidentally packages bacterial DNA and delivers it to the next cell it infects. Transformation is uptake of free DNA and conjugation uses direct contact.

Answer

D · Transduction
6.Microbiology

Answer: B · Shiga toxin-producing E. coli such as O157:H7

Why this is the answer

Shiga toxin-producing E. coli damages the bowel and the small blood vessels of the kidney, causing haemolytic uraemic syndrome. Cattle are a reservoir, so undercooked minced beef is a classic source.

Answer

B · Shiga toxin-producing E. coli such as O157:H7
7.Pharmacology

Answer: A · Apply it behind the ear several hours before travel

Why this is the answer

The patch is applied behind the ear several hours before travel, and the hands are washed afterwards. Touching the eye with drug on the fingers can dilate the pupil and blur vision.

Answer

A · Apply it behind the ear several hours before travel
8.Pharmacology

Answer: B · Paracetamol (acetaminophen)

Why this is the answer

Paracetamol passes into milk in small amounts and is widely regarded as safe. Codeine can cause dangerous opioid levels in babies of ultra-rapid metaboliser mothers, aspirin carries a Reye's risk and pethidine's metabolite accumulates in infants.

Answer

B · Paracetamol (acetaminophen)
9.Arterial blood gas interpretation

Answer: HCO₃⁻ = 27.3 mmol/L

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Change in PaCO₂

|73 − 40| = 33 mmHg → 3.3 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 1·3.3 = 27.3 mmol/L

Answer

HCO₃⁻ = 27.3 mmol/L
10.Arterial blood gas interpretation

Answer: PaCO₂ = 44.8 mmHg

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Expected PaCO₂

0.7·34 + 21 = 44.8 mmHg

Answer

PaCO₂ = 44.8 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

11.ECG rhythm strip interpretation

Answer: QTc = 0.52 s

QT and QTc: the QT interval runs from the start of the QRS complex to the end of the T wave. It shortens as the heart rate rises, so it is corrected for rate with the R–R interval in seconds: Bazett QTc = QT/√RR and Fridericia QTc = QT/∛RR. Bazett is the formula most textbooks use; it over-corrects at fast rates, where Fridericia is preferred. Limits differ between references: a QTc above about 0.45 s in men or 0.46 s in women is usually called prolonged, and above 0.50 s markedly prolonged.

Measure

QT = 13 × 0.04 = 0.52 s
RR = 25 × 0.04 = 1.00 s

Fridericia’s formula

QTc = 0.52/∛1.00 = 0.52/1 = 0.52 s

Answer

QTc = 0.52 s

Above 0.50 s: markedly prolonged. (520 ms)

12.ECG rhythm strip interpretation

Answer: pulseless electrical activity (PEA)

Pulseless electrical activity (PEA): PEA cannot be seen on a strip. The monitor shows organised electrical activity (a rhythm other than VF, VT or asystole) but the patient has no palpable pulse, so it is recognised by checking the patient. In adult resuscitation guidelines PEA and asystole are the non-shockable cardiac arrest rhythms: high-quality CPR, epinephrine as soon as possible and a search for reversible causes (the Hs and Ts, such as hypovolaemia, hypoxia, tension pneumothorax and cardiac tamponade). VF and pulseless VT are the shockable rhythms.

What the strip shows

1. Rate: R–R = 36 small boxes, 1500 ÷ 36 ≈ 42 per minute.
2. Rhythm: regular, every R–R is 1.44 s.
3. P waves: upright, one before every QRS, all alike.
4. PR interval: 0.16 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s, narrow (below 0.12 s).
sinus bradycardia

What the patient shows

no pulse despite organised electrical activity: pulseless electrical activity (PEA), a non-shockable cardiac arrest rhythm

Answer

pulseless electrical activity (PEA)

Answer

pulseless electrical activity (PEA)

PEA is recognised at the bedside, never from the strip alone. This is exam practice, not clinical guidance.

13.Evidence-based practice statistics

Answer: ARR = 19.5 %

Likelihood ratios and risk measures: LR+ = sensitivity/(1 − specificity), LR− = (1 − sensitivity)/specificity. In a trial, EER and CER are the event rates with and without treatment: RR = EER/CER, ARR = CER − EER, RRR = ARR/CER and NNT = 1/ARR, rounded up. In a case-control study only the odds ratio OR = ad/(bc) can be used. An incidence rate = new cases/person-time.

Event rates

EER = 195/1000 = 0.195
CER = 156/400 = 0.39

Absolute risk reduction

ARR = 0.39 − 0.195 = 0.195 = 19.5%

Answer

ARR = 19.5%
14.Evidence-based practice statistics

Answer: p′ = 59.4 %

Predictive values depend on prevalence: PPV = Se·p/(Se·p + (1 − Sp)(1 − p)) and NPV = Sp(1 − p)/(Sp(1 − p) + (1 − Se)p). With likelihood ratios: pre-test odds = p/(1 − p), post-test odds = pre-test odds × LR, probability = odds/(1 + odds). For a population of N, true positives = N·p·Se and false positives = N·(1 − p)·(1 − Sp). NNT = 1/(CER × RRR), rounded up.

Likelihood ratio

LR+ = 0.82/(1 − 0.86) = 5.857

Pre-test odds

0.2/(1 − 0.2) = 0.25

Post-test odds

0.25·5.857 = 1.464

Post-test probability

p′ = 1.464/(1 + 1.464) = 0.5942 ≈ 59.4%

Answer

p′ = 59.4%

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